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Finite approximants of compact totally disconnected machines. A relation- theoretic result with applications in topological algebra. (English) Zbl 0174.02903

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[1] J. Aczél andA. D. Wallace, A note on generalization of transitive systems of transformations,Colloq. Math. (to appear).
[2] A. R. Bednarek andA. D. Wallace, Relative ideals and their complements. I.,Rev. Math. Pures Appl. 11 (1966). · Zbl 0158.02504
[3] A. H. Clifford andG. B. Preston,The Algebraic Theory of Semigroups, Amer. Math. Soc. Surveys, No. 7, Providence, R.I., 1961. · Zbl 0111.03403
[4] J. M. Day andA. D. Wallace, Semigroups acting on continua (submitted). · Zbl 0158.41703
[5] S. Ginsburg, Some remarks on abstract machines,Trans. Amer. Math. Soc. 96 (1960), 400–444. · Zbl 0097.00501 · doi:10.1090/S0002-9947-60-99988-8
[6] M. L. Gluskin,Semigroups (Itogi Nauki: Algebra, Topology 1962), pp. 33–58, Moscow, 1963, (Mathematical Reviews30 (1965) #176).
[7] J. G. Hocking andG. S. Young,Topology Addison-Wesley, Reading, Mass., 1961.
[8] J. L. Kelley,General Topology Van Nostrand, Princeton, N.J., 1955.
[9] R. J. Koch andA. D. Wallace, Stability in semigroups,Duke Math. J. 24 (1957), 193–196. · Zbl 0218.22003 · doi:10.1215/S0012-7094-57-02425-0
[10] E. S. Ljapin,Semigroups, Translations of Mathematical Monographs 3, Providence, R.I., 1963.
[11] Mathematical Theory of Automata, New York, N.Y., 1963. · Zbl 0122.12705
[12] K. Numakura, Theorems on compact totally disconnected semigroups and lattices,Proc. Amer. Math. Soc. 8 (1957), 623–626. · Zbl 0081.25602 · doi:10.1090/S0002-9939-1957-0087032-5
[13] A. B. Paalman-de Miranda,Topological Semigroups, Mathematical Centre Tracts, Amsterdam, 1964.
[14] A. D. Wallace, Lectures on topological semigroups (1955–56, Notes by R. J. Koch), (1959–60, Notes by A. L. Hudson), (1961–62, Notes by A. L. Hudson), (1964–65, Notes by J. M. Day).
[15] A. D. Wallace, Relative ideals in semigroups. I. (Faucett’s Theorem),Colloq. Math. 9 (1962), 55–61. · Zbl 0100.26002
[16] A. D. Wallace, Relative ideals in semigroups. II. (The relations of Green),Acta Math. Acad. Sci. Hungar. 14 (1963), 137–148. · Zbl 0122.26802 · doi:10.1007/BF01901936
[17] A. D. Wallace, Machines with semigroup state-spaces (submitted).
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